During an election year, we see articles in the newspaper that state confidence

Question

During an election year, we see articles in the newspaper that state confidence intervals in terms percentages. For example, a poll for a particular candidate running for president might show that the candidate has 40% of the vote with a margin of error of 3 This election poll was calculated with 95% confidence. Is there a 40%chance that this candidate will be elected? There a 40% chance that this candidate will be elected, and we are 90% sure of it. There a 40% chance that this candidate will be elected, and we are 95% sure of it. Maybe. There is a 95% chance the actual vote will be between 37% and 43% There is not a 40% chance that this candidate will be elected. The proportion is 43% There is not a 40% chance that this candidate will be elected, and we are 90% sure of it. There is not a 40% chance that this candidate will be elected, and we are 95% sure of it.

Explanation / Answer

The Confidence interval here is p+- ME, where p is the proportion =40% = 40/100 =0.4 and ME is 3% = 0.03

Therefore the lower Bound is 0.4-0.03 = 0.37 and the Upper Bound is 0.4+0.03 = 0.43

Therefore the confidence interval (in %) = [37%,43%]

Now for the question: Is there a 40% chance that he will be elected?

The answer is: Maybe. There is a 95% chance that the actual vote will be between 37% and 43%. (It could be less than 40% or more than 40%)

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